 Academic journal article UNLV Gaming Research & Review Journal

# Mathematical Models of Games of Chance: Epistemological Taxonomy and Potential in Problem Gambling Research

Academic journal article UNLV Gaming Research & Review Journal

# Mathematical Models of Games of Chance: Epistemological Taxonomy and Potential in Problem Gambling Research

## Article excerpt

Introduction

What is the current place of mathematics in problem gambling research, and how can mathematics contribute toward minimizing the harmful effects of excessive gambling? In this paper, I answer the first question; then I draw upon the main principles and propose further research in the matter of the second question.

First, mathematics is strongly connected to gambling through the mathematical models1 underlying any game of chance. Games of chance are developed structurally and physically around abstract mathematical models, which are their mere essence, and the applications within these mathematical models represent the premises of their functionality. For instance, within statistical models, the house edge is ensured through precise calculations regarding expected value; if such calculations were not possible, the game would never run. Since in the research, treatment, and prevention of problem gambling we cannot separate the gambler from the game he plays, it follows that an optimal psychological intervention cannot disregard mathematics. Call this the gamblingmath indispensability principle (Barboianu, 2013b).

Determinants of the decision to gamble include not only the gambler's biological and psychological constitution, but also the structural characteristics of the gambling activity itself (Griffiths, 1993), among which games' structures are strictly related to the mathematical models of the games. Games' structures directly influence their outcomes in an idealized mathematically-modeled way - for instance, outcome volatility (see Turner, 2011) - and the behavior of outcomes is determinant for gamblers' decisions.

A second premise is the specificity of the gambling addiction through the goals of the player and the monetary reward. Although addiction is a pathological issue (and thus a medical one), the existence of the goal of winning distinguishes gambling addiction from other types of addiction and relates it to mathematics.

Thus far, the interventions involving mathematics to problem-gamblers were limited to didactical interventions, either school based or in experimental research. Past studies on the impact of a mathematical didactic intervention with gamblers, testing whether learning about mathematics of gambling does change gambling behavior, were mainly empirical (see Abbott & Volberg, 2000; Gerstein et al., 1999; Hertwig et al., 2004; Lambros & Delfabbro, 2007; Pelletier & Ladouceur, 2007; Steenbergh et al., 2004; Williams & Connolly, 2006; Peard, 2008; Turner et al., 2008a, 2008b). The content of most of the teaching modules fell within Introduction to and Basics of Probability and Statistics, covering definition and properties of probability, basics of descriptive and inferential statistics, discrete random variables, expected value, classical probability distributions, and central limit theorem. The modules were packed with examples and applications from games of chance and had lessons dedicated to demystifying mathematically the common gambling fallacies. These studies have yielded contradictory, non-conclusive results, and many of them tended unexpectedly to answer no to the hypothesis that gamblers receiving such specific mathematical education show a significant change in gambling behavior after the intervention. These studies are problematic from the standpoint of the experimental setup in three important areas: sampling, evaluation, and testing of hypotheses (Barboianu, 2013a); either of these issues may provide an explanation for the contradictory results. Aside from these issues, the following question arises: What mathematical knowledge would an optimal teaching module contain, with respect to the intended effect of limiting excessive gambling? In other words, what is missing (if anything) in the current didactic interventions? As I will show in this paper, the mathematical models and the act of mathematical modeling in gambling hold a potential for providing at least a partial answer to this question through further research. …

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